Comment #10 on issue 1850 by trel...@psu.edu: solve_linear_system contains duplicate rref algorithm
http://code.google.com/p/sympy/issues/detail?id=1850

Cool extension being able to specify the ring.  When solving underdetermined
systems, you can specify the free variables by re-ordering the variables in
ring.

Can we extend this by allowing ring to be an iterator or sequence of unknowns also? (a natural way would be to generate a ring based on the given sequence,
but I don't see how to get ring() to do this)

If this gets fixed, then perhaps we start depricating the other methods.
To summarize current state, to solve linear systems, we have

        solve(equations,unknowns)
        solve_linear_system(aug_matrix)
        solve_linear_system_LU(aug_matrix,unknowns)
        solve_poly_system(equations,unknowns)
        solve_linear(single_equation)
        polys.solvers.solve_lin_sys(equations,ring)

and

        dict(zip(unknowns,list(aug_matrix.rref()[0][:,-1])))


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